This is a phase I-II dose escalation study of 3'-azido-2,3' - dideoxyuridine (AzdU), an orally administered nucleoside analogue, in adults with HIV infection and helper T lymphocyte counts > 300/mm3. The purpose of the study is to establish a maximal tolerated dose of AzdU and in the process collect data on its potential anti-viral and immune- enhancing effects. The drug will be given for a 12 week period. Blood levels of AzdU will be obtained to establish its bioavailability and single dose versus multiple dose pharmacokinetics in humans, data will be undertaken in the CPRL.